Simulasi Monte Carlo

Anda dapat menggunakan simulasi Monte Carlo atas aset portofolio bank investasi 2005–2010 untuk menemukan VaR 95%.

Rata-rata kerugian aset terdapat dalam array Numpy mu. Matriks kovarian efisien adalah e_cov (perhatikan bahwa di sini kita menggunakan varians harian, bukan yang ditahunkan seperti pada latihan sebelumnya). Anda akan menggunakan keduanya untuk membuat lintasan sampel kerugian aset selama satu hari, guna menyimulasikan kerugian portofolio harian.

Penggunaan matriks kovarian e_cov memungkinkan lintasan aset menjadi berkorelasi, yang merupakan asumsi realistis.

Parameter simulasi total_steps disetel ke 1440, seperti pada video. Jumlah pengulangan N disetel ke 10000.

Untuk setiap pengulangan Anda akan menghitung losses kumulatif, lalu menerapkan fungsi np.quantile() untuk menemukan VaR 95%.

Bobot portofolio weights dan distribusi norm dari scipy.stats tersedia.

Latihan ini adalah bagian dari kursus

Manajemen Risiko Kuantitatif dengan Python

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Initialize daily cumulative loss for the 4 assets, across N runs
daily_loss = np.zeros((____ , N))

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Manajemen Risiko Kuantitatif dengan Python

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4.8+

Mulai Kursus Gratis

Risk management begins with an understanding of risk and return. We’ll recap how risk and return are related to each other, identify risk factors, and use them to re-acquaint ourselves with Modern Portfolio Theory applied to the global financial crisis of 2007-2008.

Exercise 1: Welcome!Exercise 2: Portfolio returns during the crisis Exercise 3: Asset covariance and portfolio volatility Exercise 4: Risk factors and the financial crisis Exercise 5: Frequency resampling primer Exercise 6: Visualizing risk factor correlation Exercise 7: Least-squares factor model Exercise 8: Modern portfolio theory Exercise 9: Practice with PyPortfolioOpt: returns Exercise 10: Practice with PyPortfolioOpt: covariance Exercise 11: Breaking down the financial crisis Exercise 12: The efficient frontier and the financial crisis

Now it’s time to expand your portfolio optimization toolkit with risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR). To do this you will use specialized Python libraries including pandas, scipy, and pypfopt. You’ll also learn how to mitigate risk exposure using the Black-Scholes model to hedge an options portfolio.

Exercise 1: Measuring Risk Exercise 2: VaR for the Normal distribution Exercise 3: Comparing CVaR and VaR Exercise 4: Which risk measure is "better"?Exercise 5: Risk exposure and loss Exercise 6: What's your risk appetite?Exercise 7: VaR and risk exposure Exercise 8: CVaR and risk exposure Exercise 9: Risk management using VaR & CVaR Exercise 10: VaR from a fitted distribution Exercise 11: Minimizing CVaR Exercise 12: CVaR risk management and the crisis Exercise 13: Portfolio hedging: offsetting risk Exercise 14: Black-Scholes options pricing Exercise 15: Options pricing and the underlying asset Exercise 16: Using options for hedging

In this chapter, you’ll estimate risk measures using parametric estimation and historical real-world data. You'll then discover how Monte Carlo simulation can help you predict uncertainty. Lastly, you’ll learn how the global financial crisis signaled that randomness itself was changing, by understanding structural breaks and how to identify them.

Exercise 1: Estimasi Parametrik Exercise 2: Estimasi parameter: Normal Exercise 3: Estimasi parameter: Skewed Normal Exercise 4: Simulasi Historis dan Monte Carlo Exercise 5: Simulasi Historis Exercise 6: Simulasi Monte Carlo

Latihan Saat Ini

Exercise 7: Pemutusan struktural Exercise 8: Pemutusan struktural krisis: I Exercise 9: Pemutusan struktural krisis: II Exercise 10: Patah struktural saat krisis: III Exercise 11: Volatilitas dan nilai ekstrem Exercise 12: Volatilitas dan break struktural Exercise 13: Nilai ekstrem dan backtesting

It's time to explore more general risk management tools. These advanced techniques are pivotal when attempting to understand extreme events, such as losses incurred during the financial crisis, and complicated loss distributions which may defy traditional estimation techniques. You’ll also discover how neural networks can be implemented to approximate loss distributions and conduct real-time portfolio optimization.

Exercise 1: Extreme value theory Exercise 2: Block maxima Exercise 3: Extreme events during the crisis Exercise 4: GEV risk estimation Exercise 5: Kernel density estimation Exercise 6: KDE of a loss distribution Exercise 7: Which distribution?Exercise 8: CVaR and loss cover selection Exercise 9: Neural network risk management Exercise 10: Single layer neural networks Exercise 11: Asset price prediction Exercise 12: Real-time risk management Exercise 13: Wrap-up and Future Steps